Existence and Stability of Traveling Waves for Infinite-Dimensional Delayed Lattice Differential Equations

2019 ◽  
Vol 26 (2) ◽  
pp. 311-331
Author(s):  
Ge Tian ◽  
Lili Liu ◽  
Zhi-Cheng Wang
Keyword(s):  
Differential Equations ◽  
Traveling Waves ◽  
Lattice Differential Equations ◽  
Infinite Dimensional ◽  
Existence And Stability

Lattice differential equations embedded into reaction–diffusion systems

2009 ◽  
Vol 139 (1) ◽  
pp. 193-207 ◽  
Author(s):  
Arnd Scheel ◽  
Erik S. Van Vleck
Keyword(s):  
Differential Equations ◽  
Invariant Manifolds ◽  
Linear Part ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Dimensional Manifold ◽  
Lattice Differential Equations ◽  
Reaction Diffusion Systems ◽  
Infinite Dimensional

We show that lattice dynamical systems naturally arise on infinite-dimensional invariant manifolds of reaction–diffusion equations with spatially periodic diffusive fluxes. The result connects wave-pinning phenomena in lattice differential equations and in reaction–diffusion equations in inhomogeneous media. The proof is based on a careful singular perturbation analysis of the linear part, where the infinite-dimensional manifold corresponds to an infinite-dimensional centre eigenspace.

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